Simulations on \(\mathbb {S}^1\)  synthetic networks with realistic parameters allow us to estimate the impact of specific topological features in the final stage of the dynamics and better gauge the expected results for real networks. Here we generated synthetic networks [1]} using the \(\mathbb {S}^1\)  model with sizes \(N=1000, 5000\) , average degree \(\langle k \rangle  = 10\)  and several \(\gamma , \beta \)  parameter values, allowing to control for the scale-freeness of the degree distribution and the mean clustering coefficient, respectively. We show the results for one of the networks in Fig. REF  and report additional results in the Supplemental.
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